1729

remembering maths on birth anniversary of Ramanujan

Yesterday, December 22nd, marked the birth anniversary of Srinivasa Ramanujan, the brilliant Indian mathematician whose intuition still amazes the world.

Although I couldn’t deliver this essay yesterday as I had to finish the blockchain series without breaking the flow, we roll math today.

Just sit back, sip your coffee, and relax.

1. Carl Friedrich Gauss

The year is roughly 1784. We are in a cramped, dusty schoolroom in Germany. The teacher, Büttner, is exhausted and wants a break. So he gives the kids what he thinks is a perfectly miserable time killing assignment.

“Add up all the numbers from 1 to 100,” he commands.

Poor kids groan and pick up their slate boards, beginning the slow, painful process:

1 + 2 = 3

3 + 3 = 6

6 + 4 = 10... ugh

The teacher relaxes, finally, at peace.

But within a few minutes, a 7-year-old boy walks up to the desk, calmly places his slate down, and sits back.

Written on that slate is one single number:

5050

The boy was Carl Friedrich Gauss, who would grow up to become the “Prince of Mathematicians.” [Cool name bruv]

The teacher was definitely furious.. at first, Surelly this kid guessed……… right?

Nope.

He realized that if you took the first number 1 and added it to the last number 100, you got 101.

2 + 99 → 101

3 + 98 → 101

There were 50 such pairs. So it wasn’t about addition, it was simple multiplication of

\(50 \text{ (pairs)} \times 101 \text{ (sum of each pair)} = 5,050\)

boom… and done.

\( \text{sum of first } n \text{ natural numbers } = \frac{n(n+1)}{2} \)

2. Srinivash Ramanujan

Fast forward a century to 1918. Ramanujan is bedridden in a hospital. His collaborator, Hardy, usually used to come visit him.

Trying to make small talk, Hardy states,

“I remember the number of my taxi,” Hardy said dully. “It was 1729. It seemed to me rather a dull number, and I hope it is not an unfavorable omen.”

Ramanujan immediately lights up,

“No, Hardy, no!” Ramanujan replied. “It is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.”

Hardy was stunned. Ramanujan didn’t calculate this on the spot; he simply knew the number intimately. He saw its personality instantly:

\(1^3 + 12^3 = 1 + 1728 = \mathbf{1729}\)

\(9^3 + 10^3 = 729 + 1000 = \mathbf{1729}\)

It starts with math

3. The Monty Hall Problem

In 1990, a magazine columnist named Marilyn vos Savant published a solution to a puzzle based on the game show Let’s Make a Deal. The response was explosive. She received over 10,000 letters, many from PhD mathematicians, yelling that she was wrong.

Here’s the setup…

You are on a game show.

Three doors

One car

Two goats

You are asked to pick a door behind which you think is the car. You pick door 1

Monty Hall opens 1 of the remaining doors, revealing a goat.

Now, 2 doors, one you chose, one you didn’t remain.

Then he asks you, “Wanna Switch?”

As a normal human, you think, 2 doors, one of which hides a car, so 50-50 chance on each door, switch doesn’t matter.

Except…. it does.

Let’s stretch the problem here,

Imagine not 3, but 100 doors

You pick 1, odds you’re right are 1%

But the odds that the car is behind any of the remaining doors are 99%

Monty knows all the doors and opens 98 out of the doors that had a goat.

Leaving 1 door competing with your choice.

Would you remain on your 1% choice?

Exactly, the other side had a 99% chance of a car.

Always switch to increase your chances.

And that’s a wrap for today, and before I say goodbye for today, here’s a quote by Albert Camus I’ve been pondering,

“Those who lack the courage will always find a philosophy to justify it."

Please don’t forget to share it with your friends, family, and strangers.

Have a Great Day 💖